We cast some classes of fitness landscapes as problems in spectral analysis on various Cayley graphs. In particular, landscapes derived from RNA folding are realized on Hamming graphs and analyzed in terms of Walsh transforms; assignment problems are interpreted as functions on the symmetric...

In many complex systems control situations, searching for solutions or alternatives is involved. Searching for solutions can be modeled by a search on a fitness landscape. Knowing the structure of the underlying landscape can help in explaining or predicting aspects of an actual seach on it, and...

We introduce a class of embedded-particle models for describing the emergent computational strategies observed in cellular automata (CAs) that were evolved for performing certain computational tasks. The models are evaluated by comparing their estimated performances with the actual performances...

A correlation analysis will be applied to subspaces of the fitness landscape generated by the synchronization task for one- dimensional cellular automata. This results in a stochastic model that can be used to characterize the correlation structure of those subspaces. The results show that both...

Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number of distinct products that these interactions can...

The structure of a fitness landscape is still an ill-defined concept. This paper introduces a statistical fitness landscape analysis, that can be used on a multitude of fitness landscapes. The result of this analysis is a statistical model that, together with some statistics denoting the...

In our work we are studying how genetic algorithms (GAs) can evolve cellular automata (CAs) to perform computations that require global coordination. The "evolving cellular automata" framework is an idealized means for studying how evolution (natural or computational) can create systems that...

The distinction between continuous and discontinuous transitions is a long-standing problem in the theory of evolution. Continuity being a topological property, we present a formalism that treats the space of phenotypes as a (finite) topological space, with a topology that is derived from the...

We present a method for approximating a fitness landscapes as a superposition of "elementary" landscapes. Given a correlation function of the landscape in question we show that the relative amplitudes of contributions with P-ary interactions can be computed. We show an application to RNA free...

The set R of relevant cycles of a graph G is the union of its minimum cycle bases. We introduce a partition of R such that each cycle in a class W can be expressed as a sum of other cycles and W and shorter cycles. It is shown that each minimum cycle basis contains the same number of...